Write the domain of the real function f defined by

We have,

$f(x)=\sqrt{25-x^{2}}$

The function is defined only when $25-x^{2} \geq 0$

$\Rightarrow x^{2}-25 \leq 0$

$\Rightarrow(x+5)(x-5) \leq 0$

$\Rightarrow x \in[-5,5]$

So, the domain of the given function is $[-5,5]$.